Simplify the Radical Expression -1/4 square root of 48x^3

$- \frac{1}{4} \sqrt{48 x^{3}}$

Step 1

Rewrite $48 x^{3}$ as ${(4 x)}^{2} \cdot (3 x)$ .

Factor $16$ out of $48$ .

$- \frac{1}{4} \sqrt{16 (3) x^{3}}$

Rewrite $16$ as $4^{2}$ .

$- \frac{1}{4} \sqrt{4^{2} \cdot 3 x^{3}}$

Factor out $x^{2}$ .

$- \frac{1}{4} \sqrt{4^{2} \cdot 3 (x^{2} x)}$

Move $3$ .

$- \frac{1}{4} \sqrt{4^{2} x^{2} \cdot 3 x}$

Rewrite $4^{2} x^{2}$ as ${(4 x)}^{2}$ .

$- \frac{1}{4} \sqrt{{(4 x)}^{2} \cdot 3 x}$

Add parentheses.

$- \frac{1}{4} \sqrt{{(4 x)}^{2} \cdot (3 x)}$

Step 2

Pull terms out from under the radical.

$- \frac{1}{4} (| 4 x | \sqrt{3 x})$

Step 3

Remove non-negative terms from the absolute value.

$- \frac{1}{4} (4 | x | \sqrt{3 x})$

Step 4

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{- 1}{4} (4 | x | \sqrt{3 x})$

Factor $4$ out of $4 | x | \sqrt{3 x}$ .

$\frac{- 1}{4} (4 (| x | \sqrt{3 x}))$

Cancel the common factor.

$\frac{- 1}{4} (4 (| x | \sqrt{3 x}))$

Rewrite the expression.

$- 1 (| x | \sqrt{3 x})$

Step 5

Rewrite $- 1 (| x | \sqrt{3 x})$ as $- (| x | \sqrt{3 x})$ .

$- | x | \sqrt{3 x}$